A seller knows that there are two bidders for the object he is selling. He believes that with probability 1/2, one has a buyer value of $5 and the other has a buyer value of $7 and, with probability 1/2, one has a buyer value of $3 and the other has a buyer value of $10. He knows that bidders will want to buy the object so long as they can get it for their buyer value or less. He sells it in an English auction with a reserve price which he must set before the auction starts. To maximize his expected profits, he should set the reserve price at:

Reserve price = $6.25

Approximately $7

Explanation:

Reserve price is the lowest set price that is acceptable by a seller at an auction.

With probability 1/2:

Buyer values = $5 and $7

Buyer values= $3 and $10

Since the seller knows there are two bidders for the object he is selling and he wants to maximize his expected profits. He also sells it in an English auction which he must set the reserve price before the commencement of the auction. His reserve price should be:

= (1.25 + 1.75) + (0.75 + 2.5)

= 3 + 3.25

$6.25

The maximize his expected profit the buyer should set his reserve price at approximately $7

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